The other example was in civilization they showed percentage chances of winning a battle. ... This means actually weighting the percentages differently from what the player is told
This is a (persistent) myth. None of the Civilization games actually do this. Civilization 4 is the only game in the series that displays combat prediction as a percentage chance, and the source code for Civ 4's combat engine is publicly released and well understood. (I am a developer on a Civ 4 modding project and familiar with the code.) The earlier Civ games before 4 don't display any kind of combat odds, and Civ 5 has a totally different system that isn't based on winning percentage. So, unless you're talking about some other game like Galactic Civilizations or a mod for Civilization 4, this isn't true.
Your underlying point is certainly true, though: gameplay often is perceived as a better experience with "randomness" smoothed out to produce more uniformly distributed results.
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The other example was in civilization they showed percentage chances of winning a battle. ... This means actually weighting the percentages differently from what the player is told
This is a (persistent) myth. None of the Civilization games actually do this. Civilization 4 is the only game in the series that displays combat prediction as a percentage chance, and the source code for Civ 4's combat engine is publicly released and well understood. (I am a developer on a Civ 4 modding project and familiar with the code.) The earlier Civ games before 4 don't display any kind of combat odds, and Civ 5 has a totally different system that isn't based on winning percentage. So, unless you're talking about some other game like Galactic Civilizations or a mod for Civilization 4, this isn't true.
Your underlying point is certainly true, though: gameplay often is perceived as a better experience with "randomness" smoothed out to produce more uniformly distributed results.